4 Answers
4

Out of the box, no, posts can't have parents. They can be assigned to categories, which can be organised hierarchically. Pages, however, can have parents and you can build a menu structure out of them by using that feature.

As to where this is enforced: The parent of a post is stored in the column "post_parent" in "wp_posts". It's not really enforced as such, just the default UI doesn't give you an option to set it and default WP coding doesn't use that value for Posts. It wouldn't be too difficult to create a custom post type to have posts with parents though.

I know this is an old post. However none of these answers are correct, and I wanted to post the solution I used to solve this problem. The best way to set a parent page through all of your posts is through the (Appearance -> Customize) menu. You can set a static page for your home page or posts page. When you set a static post page, that page will be the parent for every individual blog post.

That's not a parent page - it's a template containing an archive of posts. Setting that up doesn't make posts hierarchical.
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kaiser♦Apr 2 '14 at 11:24

How is that not a parent page? It's a static page (which by the way does not have to be an archive, whatever page template you assign to that static page, can have whatever you want), and when this is set up your urls follow that hierarchy, as well as Breadcrumbs on the site. It's a 1 minute fix that allows you to assign a static page as the post parent. His question mentions NOTHING about it being hierarchical in the first place. Perhaps you could enlighten me on how this solution would be bad practice?
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LateToThePartyApr 6 '14 at 15:11

"Are posts supposed to have parent" is the same thing as "Are posts hierarchical". A template can contain everything, but the plain fact that it contains a loop that returns and displays an archive loop does not (a) make the page its parent (it's just the place where the loop happens to be) and (b) does not make the built in post type "post" hierarchical or in other words, does not assign a parent. But yes, you can summon posts in a loop by specific criteria (like a shared child-category).
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kaiser♦Apr 6 '14 at 16:19

Don't get thrown off by criticism or clarification of your question or answer. This place is something where this actually needs to happen all the time to make the best answers succeed and serve as wiki/library place where one can go and instantly figure out how to do something or get as much possible insights on how something works. We even encourage people (like you) to comment on other answers as well. Keep in mind that I nowhere mentioned that your answer is bad practice. It's true in a lot of ways, just the statement that it makes the post type hierarchical isn't.
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kaiser♦Apr 6 '14 at 16:21